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Ronal asked 100 students to choose their favorite subject from among mathematics history and our she found that 22 students kill

Llana [10]

Answer:

I think 52% of students chose art

Step-by-step explanation:

7 0

3 years ago

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20 hours, standard deviation of 6:

This means that $\mu = 20, \sigma = 6$

Sample of 150:

This means that $n = 150, s = \frac{6}{\sqrt{150}}$

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}$

$Z = 2.04$

$Z = 2.04$ has a p-value of 0.9793

X = 19.5

$Z = \frac{X - \mu}{s}$

$Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}$

$Z = -1.02$

$Z = -1.02$ has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

3 0

3 years ago

(Score for Question 2: ___ of 5 points)

GuDViN [60]

Answer:

Since you don't show your triangles, I'm guessing it is this one...?

△DWP D = (-2, 4), W = (-1, 2), P = (3, 3)

△MJS M = (-4, -4), J = (-2, -3), S = (-3, 1)

There are 2 steps:

1. 90° counterclockwise rotation about the origin

2. Translation downward 2 units

Step-by-step explanation:

1. 90° counterclockwise rotation about the origin = (x, y) to (-y, x),

D moves from (-2, 4) to (-4, -2)

W moves from (-1, 2) to (-2, -1)

P moves from (3, 3) to (-3, 3)

2. Translation downward 2 units = (x, y) to (x, y-2),

D moves from (-4, -2) to (-4, -4) = M

W moves from (-2, -1) to (-2, -3) = J

P moves from (-3, 3) to (-3, 1) = S

Therefore △DWP IS congruent to △MJS.

4 0

2 years ago

Rachel is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove to get to the

lara31 [8.8K]

Answer:

$D(t)=-24t+166$

Step-by-step explanation:

Let

D(t) = the distance to the safe zone (measured in meters)

t = time (measured in seconds)

<u>Given:</u>

Rachel's rate = 24 meters per second

At $t_1=4$ seconds $D(t_1)=70$ meters

<u>Find:</u> D(t)

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative.

Hence, the function expression is

$D(t)=-24t+b$

To find b, substitute $t_1=4$ and $D(t_1)=70:$

$70=-24\cdot 4+b\\ \\70=-96+b\\ \\b=70+96\\ \\b=166$

So,

$D(t)=-24t+166$

7 0

3 years ago

Apply the following transformations to the shape and draw the resulting shape

Morgarella [4.7K]

Answer:

Step-by-step explanation:

Take the coordinates(0,0)(2, -2)(6, -4)(4, -6) and cut each number in half. Then move each point left 3 and up 2.

4 0

3 years ago